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noc20 ma20 lec51 Zariski Topology on arbitrary commutative rings
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Classroom Contents
Introduction to Algebraic Geometry and Commutative Algebra
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- 1 Intro Introduction to Algebraic Geometry and Commutative Algebra
- 2 noc20 ma20 lec01 Motivation for K algebraic sets
- 3 noc20 ma20 lec02 Definitions and examples of Affine Algebraic Set
- 4 noc20 ma20 lec03 Rings and Ideals
- 5 noc20 ma20 lec04 Operation on Ideals
- 6 noc20 ma20 lec05 Prime Ideals and Maximal Ideals
- 7 noc20 ma20 lec06 Krull's Theorem and consequences
- 8 noc20 ma20 lec07 Module, submodules and quotient modules
- 9 noc20 ma20 lec08 Algebras and polynomial algebras
- 10 noc20 ma20 lec09 Universal property of polynomial algebra and examples
- 11 noc20 ma20 lec10 Finite and Finite type algebras
- 12 noc20 ma20 lec11 K Spectrum K rational points
- 13 noc20 ma20 lec12 Identity theorem for Polynomial functions
- 14 noc20 ma20 lec13 Basic properties of K algebraic sets
- 15 noc20 ma20 lec14 Examples of K algebraic sets
- 16 noc20 ma20 lec15 K Zariski Topology
- 17 noc20 ma20 lec16 The map VL
- 18 noc20 ma20 lec17 Noetherian and Artinian Ordered sets
- 19 noc20 ma20 lec18 Noetherian induction and Transfinite induction
- 20 noc20 ma20 lec19 Modules with Chain Conditions
- 21 noc20 ma20 lec20 Properties of Noetherian and Artinian Modules
- 22 noc20 ma20 lec21 Examples of Artinian and Noetherian Modules
- 23 noc20 ma20 lec22 Finite modules over Noetherian Rings
- 24 noc20 ma20 lec23 Hilbert’s Basis TheoremHBT
- 25 noc20 ma20 lec24 Consequences of HBT
- 26 noc20 ma20 lec25 Free Modules and rank
- 27 noc20 ma20 lec26 More on Noetherian and Artinian modules
- 28 noc20 ma20 lec27 Ring of FractionsLocalization
- 29 noc20 ma20 lec28 Nil radical, contraction of ideals
- 30 noc20 ma20 lec29 Universal property of S 1A
- 31 noc20 ma20 lec30 Ideal structure in S 1A
- 32 noc20 ma20 lec31 Consequences of the Correspondence of Ideals
- 33 noc20 ma20 lec32 Consequences of the Correspondence of IdealsContd
- 34 noc20 ma20 lec33 Modules of Fraction and universal properties
- 35 noc20 ma20 lec34 Exactness of the functor S 1
- 36 noc20 ma20 lec35 Universal property of Modules of Fractions
- 37 noc20 ma20 lec36 Further properties of Modules and Module of Fractions
- 38 noc20 ma20 lec37 Local Global Principle
- 39 noc20 ma20 lec38 Consequences of Local Global Principle
- 40 noc20 ma20 lec39 Properties of Artinian Rings
- 41 noc20 ma20 lec40 Krull Nakayama Lemma
- 42 noc20 ma20 lec41 Properties of IK and VL maps
- 43 noc20 ma20 lec42 Hilbert’s Nullstelensatz
- 44 noc20 ma20 lec43 Hilbert’s NullstelensatzContd
- 45 noc20 ma20 lec44 Proof of Zariski’s LemmaHNS 3
- 46 noc20 ma20 lec45 Consequences of HNS
- 47 noc20 ma20 lec46 Consequences of HNSContd
- 48 noc20 ma20 lec47 Jacobson Ring and examples
- 49 noc20 ma20 lec48 Irreducible subsets of Zariski TopologyFinite type K algebra
- 50 noc20 ma20 lec49 Spec functor on Finite type K algebras
- 51 noc20 ma20 lec51 Zariski Topology on arbitrary commutative rings
- 52 noc20 ma20 lec52 Spec functor on arbitrary commutative rings
- 53 noc20 ma20 lec53 Topological properties of Spec A
- 54 noc20 ma20 lec54 Example to support the term “Spectrum”
- 55 noc20 ma20 lec55 Integral Extensions
- 56 noc20 ma20 lec56 Elementwise characterization of Integral extensions
- 57 noc20 ma20 lec57 Properties and examples of Integral extensions
- 58 noc20 ma20 lec58 Prime and Maximal ideals in integral extensions
- 59 noc20 ma20 lec59 Lying over Theorem
- 60 noc20 ma20 lec60 Cohen Siedelberg Theorem
